Problem 2 The position of a hard drive head is described by the state space model dx dt = y= (-2.5 0) x + (8) u (01) x a. Determine a state feedback u=-Lx+l,r which places the poles of the closed loop system in s = -4 4i and results in static gain 1 from reference to output. b. Determine a Kalman filter d = At+Bu+K(y- C) dt for the system. Briefly motivate necessary design choices.